Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size. r=−0. 595, α=0. 05, n=17

Answer:

∠a=40°, ∠b=50°, ∠c=115°.

Step-by-step explanation:

∵The opposite vertex angles are equal,

∴∠a=40°.

∴∠b=90°-∠a=90°-40°=50°.

∠c=180°-65°=115°.

the area and volume of the Pyramid of Gaza are  139, 840 m²

and 52950 m³ respectively.

The formula for volume and area of a square pyramid are given thus;

Volume, V= [tex]a^2\frac{h}{3}[/tex]

Area , [tex]A=a^2+2a \sqrt{\frac{a^2}{4}+ h^2 }[/tex]

Where

Substitute the values;

Area = [tex]230^2 + 2(230) \sqrt{\frac{230^2}{4}+ 150^2 }[/tex]

Area = [tex]52900 + 460 + \sqrt{13225 + 22500}[/tex]

Area = [tex]52900 + 460(189)[/tex]

Area = 52900 + 86, 940

Area = 139, 840 m²

Volume , v = [tex]230^2 + \frac{150}{3}[/tex]

Volume = 52900 + 50

Volume = 52950 m³

Thus, the area and volume of the Pyramid of Gaza are  139, 840 m²

and 52950 m³ respectively.

Learn more about a square pyramid here:

https://brainly.com/question/9071478

#SPJ1

answer is in the attachment below

goodluck!!

The Distance - Time graph that represents that represents Charlie's trip is attached accordingly.

A distance-time graph can be used to illustrate the distance traveled by an item moving in a straight line.

The gradient of the line in a distance-time graph equals the speed of the item. The quicker the item moves, the higher the gradient (and the steeper the line).

Some of the uses of the distance-time graph are;

Learn more about Distance - Time Graph:
https://brainly.com/question/19730285
#SPJ1

Answer:

11/18.

Dan is 8.

Step-by-step explanation:

The initial fraction is

x / 2x-4

Adding 3/3 we have

x+3 / 2x-1 = 2/3

Cross multiply:

3(x+3) = 2(2x-1)

3x + 9 = 4x - 2

9 + 2 = 4x - 3x

11 = x,

So the original fraction was 11 / 2(11) - 4

= 11/18.

If Dans age is d then Lois's age = 4d.

So 4d + d  = 40

5d = 40

d = 8.

So Dan is 8 years old.

The line is parallel to y axis

We know that if a line is parallel to y axis

So there is no slope

Here it has constant x value as -2

So the equation is

Option A

Answer:

x = -2

Step-by-step explanation:

The line is crossing the x-axis at -2, The graph is attached

Since it is identical to the graph given in the problem, x=-2 is the correct answer

Answer:

y = 2x + 7

Step-by-step explanation:

When a line is parallel to another line, then the slopes of the lines are equal. If line A has an equation y = 3x + 5, then line B, parallel to line A, must also have a slope of 3. Therefore, we know that m (slope) is 2 in this case.

Next, let’s substitute the x and y coordinates and the slope value into y - y1 = m(x - x1). In this case, -4 is x1, and -1 is y1.

y - y1 = m(x - x1)

y + 1 = 2(x + 4)

Finally, simplify the equation and transform it into the slope intercept form, y = mx + b.

y + 1 = 2(x + 4)
y + 1 = 2x + 8

y = 2x + 7

The end behavior of the function is as:

as →∞, f(x)→+∞ and as x→-∞, f(x)→+∞

The x-axis "endpoints" of a function's graph are referred to as its "end behavior" in this context.

choosing the polynomial function's greatest degree. The highest degree term will dominate the graph since it will expand more quickly than the other terms as x gets very big or very small.

Function f(x)=2∛x has the following graph:

The behavior of the function at its conclusion is because it leads to infinity.

as  x→∞, f(x)→+∞ and as x→-∞, f(x)→+∞

To know more about  behavior of a function visit:

https://brainly.com/question/14361710

#SPJ4

Answer:

0.5%

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Original form:

y=mx+b

m=slope

b=y interecept

By replacing those variables with the given we come up with the equation of:

y=3/2x-7

Answer:B

Step-by-step explanation:

The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

At point (0, 8):

8 = ab⁰

a = 8

At point (1, 32):

32 = 8b

b = 4

The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer + Step-by-step explanation:

10 × 5 × 2

= 10 × (5 × 2)   (associative property)

= 10 × (10)

= 10 × 10

= 100

The way to solve this is to try to get the vales that would best fill the empty spaces in the diagram. This has been done below

a. log6⁰, log 2 . 1, log 8/3

b. log 1 .4 , 1 , log 4. 6

c. log 9/2, log 3. 5 , log 5⁷

To do this, you have to decide on that specific  number whose logarithm you are trying to determine. Next you have to find the base of that number.

The logarithm of the number is the power that it would have to be raised for us to obtain a different number.

Read more on the logarithm of a number here: brainly.com/question/1807994

#SPJ1

The standard matrix for the linear transformation t is

| 3     6 |

| 3    -6 |

The linear transformation of matrix T is given as:

t(x, y) = (3x + 6y, 3x − 6y)

When the above linear transformation is represented as a matrix, we have the following expression

T([x]) =   | 3x + 6y |

  [y]       | 3x  - 6y |

The above linear transformation of matrix can be rewritten as the following product of matrixes

T([x]) =   | 3x + 6y | = | 3     6 | | x |

  [y]       | 3x  - 6y |    | 3    -6 | | y |

From the above equation, the standard matrix for the linear transformation t is

| 3     6 |

| 3    -6 |

Hence, the standard matrix for the linear transformation t is

| 3     6 |

| 3    -6 |

Read more about matrix at:

https://brainly.com/question/11989522

#SPJ1

The ratio of the volume of a pyramid to the volume of a prism with the same base and height is 1 to 3; the formula for the volume of a pyramid is V = 1/3Bh.

where,

Volume of prism : Volume of pyramid

Bh : 1/3Bh

Therefore, the ratio of the volume of a pyramid to the volume of a prism with the same base and height is 1 to 3.

Learn more about volume of pyramid:

https://brainly.com/question/18994842

#SPJ1

Answer:

< B.

Step-by-step explanation:

B  corresponds to F.

Answer:

below

Step-by-step explanation:

1) 8 = 25 percent

100 percent = 8 x 4

100 percent = 32

2) 8 = 75 percent

5 percent = 8 / 15

100 percent = 8 / 15 x 20

100 percent = 10.67

3) x = weight of puppy A

y = percentage

z = adult weight

z = x(100 / y)

Answer:

48/80 = 6/10

Step-by-step explanation:

 48 wins

+ 32 lost

= 80 total games

Then the fraction of the games win is:

48/80

= 6/10

Answer:3/5 of the games

Step-by-step explanation: The total number of games played by the team is 48+32 = 80 games. out of hose 80, they won 48 so they won 48/80 games. We can simplify this by dividing both sides by 8 to get 6/10. Which is 60%. Finally we can simplify again by dividing the fraction by 2/2 to get 3/5.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Find inverse of given function :

[tex]\qquad❖ \: \sf \:y = \sqrt{x} + 7[/tex]

[tex]\qquad❖ \: \sf \: \sqrt{x} = y - 7[/tex]

[tex]\qquad❖ \: \sf \:x = (y - 7) {}^{2} [/tex]

Next, replace x with f-¹(x) and y with x ~

[tex]\qquad❖ \: \sf \:f {}^{ - 1} (x) = (x - 7) {}^{2} [/tex]

we got our inverse function.

Condition : x should be greater or equal to 7

because we will get same value of y for different x if we also include values less than 7.

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

[tex]\longrightarrow\bold{f(x)= \sqrt{7}}[/tex]

To solve for the inverse of a function we begin by re-writing the function as an equation in terms of y.

[tex]\bold{Becomes,}[/tex]

Next step we switch sides for x and y variables and then solve for the y variable as shown below,

[tex]\longrightarrow\sf{y= \sqrt{x}+7}[/tex]

[tex]\bold{Then,}[/tex]

[tex]\longrightarrow\sf{x= \sqrt{y}+7}[/tex]

[tex]\small\bold{Solve \: for \: y \: and \: subtract \: 7 \: from \: the \: both \: }[/tex] [tex]\bold{sides,}[/tex]

[tex]\longrightarrow\sf{x-7= \sqrt{y}}[/tex]

[tex]\small\bold{Square \: both \: sides }[/tex]

[tex]\sf{(x-7)^2=(\sqrt{y})^2}[/tex]

[tex]\sf{(x-7)^2=y}[/tex]

We now re-write in function notation. Take note however that this is the inverse:

[tex]\bold{Where \: y}[/tex] [tex]\sf{=(x-7)^2 }[/tex]

[tex]\longrightarrow\sf{y= (x-7)^2 }[/tex]

[tex]\huge\mathbb{ \underline{ANSWER:}}[/tex]

[tex]\large\boxed{\sf A. \: \: f^{-1}(x)= (x − 7)^2 , \: for \: \underline > 7 }[/tex]

The given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.

According to the given question.

We have a sequence,

[tex]a_{n} = 2^{\frac{1}{n} }[/tex]

Since, we know that

The sequence of real numbers [tex]S_{n}[/tex], where n goes from 1 to infinity has a limit L, the the sequence is convergent to L. If the sequence doesn't have limit then it is divergent.

The nth root function is strictly increasing for positive real values.

Therefore,

[tex]1^{\frac{1}{n} } \leq 2^{\frac{1}{n} } \leq n^{\frac{1}{n} }[/tex]           [tex]\forall \ n\geq 2[/tex]

Also,

[tex]\lim_{n \to \infty} n^{\frac{1}{n} } = 1[/tex]

[tex]\implies \lim_{n \to \infty} 1^{\frac{1}{n} } =1[/tex]   ( by squeeze theorem)

Thereofore,

[tex]\lim_{n \to \infty}2^{\frac{1}{n} } =1[/tex]

So, the given sequecence has a limit i.e. 1. Which means [tex]2^{\frac{1}{n} }[/tex] is a convergent sequence.

Hence, the given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.

Find out more information about convergent and divergent sequence here:

https://brainly.com/question/15415793

#SPJ4

Answer:

(15,0) , (0,6)

Step-by-step explanation:

Same concept as the previous 2 questions.

x-intercept is where the line touches the x-axis, and y = 0.

when y = 0,

12x + 30(0) = 180

12x = 180

x = [tex]\frac{180}{12}[/tex]

x = 15

Therefore the coordinates of the x-intercept is (15,0)

y-intercept is where the line touches the y-axis, and x = 0.

when x = 0,

12(0) + 30y = 180

30y = 180

y = [tex]\frac{180}{30}[/tex]

y = 6

Therefore the coordinates of the y-intercept is (0,6)

The power series  is

g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....

To deduce the power series of g(x) from the power series for f(x) and identify its radius of convergence

The power series for f(x) is just the geometric series derived from 1/1-y ,setting y=2x.

Its radius of convergence is 0.5

Let,

f(x)= 1/1-2x = 1+ (2x) + (2x)2 + .........+(2x)n......+....

The power series expansion (geometric series),

valid for I2xI < 1 , IxI < 0.5

so, radius of convergence = 0.5

The power series for g(x) is found by integrating term by term the power series of f(x) (upto a constant). The radius of converngence of g(d) is the same as that of f(x) (from general theory) =0.5

Now, g(x) = ln(1-2x)

= -2 [tex]\int\limits^a_b {(1/1-2x)} \, dx = -2 \int\limits^a_b {f(x)} \, dx[/tex]

=-2 [tex]\int\limits^a_b {[1+(2x)+ (2x)2 +........+ (2x)n+.......]} \, dx[/tex]

g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....

is the power series expansion for g(x).

radius of convergence =0.5

For more information about power series, visit

https://brainly.com/question/17225810

#SPJ4

Answer:

student 2 is correct

Step-by-step explanation:

there are 10 [tex]\frac{1}{10}[/tex] ' s in 1 , so

37 × 10 = 370 ← number of tenths in 37

0.6 = [tex]\frac{6}{10}[/tex] , that is 6 tenths

then

37.6 = 370 + 6 = 376 ← number of tenths

Answer: D

Step-by-step explanation:

The first term is 3 and the common difference is 2.

Substituting into the explicit formula for an arithmetic sequence gives D as the correct answer.

Answer:

  see attached

Step-by-step explanation:

Each grid square represents 5 m, so the distances shown on the grid will be scaled appropriately.

The 25 m base dimension will be represented by (25 m)/(5 m/square) = 5 squares.

The 30 m height dimension will be represented by (30 m)/(5 m/square) = 6 squares.

The attached drawing shows the triangle with base 25 m and height 30 m on a 5 m grid.

The sum of the first 40 terms of the geometric sequence is:

22,114,662.64

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The sum of the first n terms of a sequence is:

[tex]S_n = \frac{a_1(1 - q^n)}{1 - q}[/tex]

For this problem, the parameters are:

a1 = 1, q = 1.5, n = 40.

Hence the sum is:

[tex]S_{40} = \frac{1 - 1.5^{40}}{1 - 1.5} = 22,114,662.64[/tex]

More can be learned about geometric sequences at https://brainly.com/question/11847927

#SPJ1

Answer:

a)  2x + 4

b)  2x + 5

c)  8

d)  9

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=x+1\\g(x)=2x+3 \end{cases}[/tex]

Function composition is an operation that takes two or more functions and combines them into a single function.

(f o g)(x) means find g(x) first and then substitute the result into f(x).

(g o f)(x) means find f(x) first and then substitute the result into g(x).

Part (a)

[tex]\begin{aligned}(f \circ g)(x) & = f[g(x)]\\& = g(x)+1\\ & = (2x+3)+1\\& = 2x+4\end{aligned}[/tex]

Part (b)

[tex]\begin{aligned}(g \circ f)(x) & = g[f(x)]\\& = 2[f(x)]+3\\& = 2(x+1)+3\\ & = 2x+2+3\\& = 2x+5\end{aligned}[/tex]

Part (c)

[tex]\begin{aligned}(f \circ g)(2) & = f[g(2)]\\& = g(2)+1\\ & = (2(2)+3)+1\\ & = (4+3)+1\\& = 8\end{aligned}[/tex]

Part (d)

[tex]\begin{aligned}(g \circ f)(2) & = g[f(2)]\\& = 2[f(2)]+3\\& = 2(2+1)+3\\ & = 2(3)+3\\ & = 6+3\\& = 9\end{aligned}[/tex]

Learn more about composite functions here:

https://brainly.com/question/27966754

https://brainly.com/question/28062427

(fog)(x)

(gof)(x)

(fog)(2))

(gof)(2)

Answer:

(-1,1)

Step-by-step explanation:

look where the two equations intercept that is usually the answer

The linear equation can represent the ages of two sisters that are born one-year apart.

Here we have the linear equation:

y = x + 1

So the value of y is always one more than the value of x, so for example, suppose that two sisters are born one-year appart, then we can use the above linear equation to represent the age of the older sister as a function of the age of of the younger one.

In that case, the slope of 1 means that both of the sisters age at the same ritm.

The y-intercept of 1 means that the older sister is 1 years old when the younger sister was born.

If you want to learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Answer:

[tex]\boxed{\sf 1\dfrac{1}{6}\ liters \ of \ water}[/tex]

Explanation:

Let the total water required water the entire ground be g

Equation:

[tex]\sf \dfrac{2}{7}\:g = \dfrac{1}{3} \ liters \ of \ water[/tex]

rearranging

[tex]\sf g = \dfrac{7(1)}{3(2)}[/tex]

simplify

[tex]\sf g = \dfrac{7}{6} \ liters \ of \ water[/tex]

rewrite in mixed fraction

[tex]\bf g = 1\dfrac{1}{6}\ liters \ of \ water[/tex]

The water required to water the entire ground is  1 1/6 liters.